Stopping Criteria for the Iterative Solution of Linear Least Squares Problems
نویسندگان
چکیده
منابع مشابه
Stopping Criteria for the Iterative Solution of Linear Least Squares
We explain an interesting property of minimum residual iterative methods for the solution of the linear least squares (LS) problem. Our analysis demonstrates that the stopping criteria commonly used with these methods can in some situations be too conservative, causing any chosen method to perform too many iterations or even fail to detect that an acceptable iterate has been obtained. We propos...
متن کاملLinear regression models, least-squares problems, normal equations, and stopping criteria for the conjugate gradient method
Minimum-variance unbiased estimates for linear regression models can be obtained by solving leastsquares problems. The conjugate gradient method can be successfully used in solving the symmetric and positive definite normal equations obtained from these least-squares problems. Taking into account the results of Golub and Meurant (1997, 2009) [10,11], Hestenes and Stiefel (1952) [17], and Strako...
متن کاملPreconditioned Iterative Methods for Solving Linear Least Squares Problems
New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU fa...
متن کاملLinear Least Squares Problems
A fundamental task in scientific computing is to estimate parameters in a mathematical model from collected data which are subject to errors. The influence of the errors can be reduced by using a greater number of data than the number of unknowns. If the model is linear, the resulting problem is then to “solve” an in general inconsistent linear system Ax = b, where A ∈ Rm×n and m ≥ n. In other ...
متن کاملConvexly constrained linear inverse problems: iterative least-squares and regularization
| In this paper, we consider robust inversion of linear operators with convex constraints. We present an iteration that converges to the minimum norm least squares solution; a stopping rule is shown to regularize the constrained inversion. A constrained Laplace inversion is computed to illustrate the proposed algorithm.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2009
ISSN: 0895-4798,1095-7162
DOI: 10.1137/080724071